hiker starts at his camp and moves the following distances while exploring his surroundings:75.0 m north, 2.50102 m east, 125 m at an angle 30.0° north of east, and 1.50102 m south.(a) Find his resultant displacement from camp. (Take east as the positive x-direction and north asthe positive y-direction.)

To solve this problem, we need to break down each movement into its x (east-west) and y (north-south) components and then add them up to find the total displacement in each direction.

1. The first movement is 75.0 m north. This is entirely in the y direction, so it adds 75.0 m to the y displacement and 0 m to the x displacement.

2. The second movement is 2.50 x 10^2 m east. This is entirely in the x direction, so it adds 2.50 x 10^2 m to the x displacement and 0 m to the y displacement.

3. The third movement is 125 m at an angle 30.0° north of east. We can use trigonometry to break this down into x and y components. The x component is 125 m * cos(30.0°) = 108.25 m, and the y component is 125 m * sin(30.0°) = 62.5 m.

4. The fourth movement is 1.50 x 10^2 m south. This is entirely in the y direction, but it's in the negative y direction, so it subtracts 1.50 x 10^2 m from the y displacement and adds 0 m to the x displacement.

Now we can add up the x and y displacements to find the total displacement. The x displacement is 2.50 x 10^2 m + 108.25 m = 358.25 m. The y displacement is 75.0 m + 62.5 m - 1.50 x 10^2 m = 37.5 m.

The total displacement is then the square root of the sum of the squares of the x and y displacements, which is sqrt((358.25 m)^2 + (37.5 m)^2) = 361.77 m.

The direction of the displacement is the arctangent of the y displacement divided by the x displacement, which is arctan(37.5 m / 358.25 m) = 5.97° north of east.

So, the hiker's resultant displacement from camp is 361.77 m at an angle of 5.97° north of east.